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Existence of solutions for the Boussinesq system of equations. (English) Zbl 0476.35067


MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35G25 Initial value problems for nonlinear higher-order PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35L05 Wave equation
35B20 Perturbations in context of PDEs
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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References:

[1] Benjamin, T. B., (Newell, A. C., Lectures on Nonlinear Wave Motion. Lectures on Nonlinear Wave Motion, Lectures in Applied Mathematics, Vol. 15 (1974), Amer. Math. Soc.: Amer. Math. Soc. Providence, R. I.)
[2] Bona; Smith, A model for the two way propagation of water waves in a channel, (Math. Proc. Cambridge Philos. Soc., 79 (1976)), 167 · Zbl 0332.76007
[3] Dunford-Schwartz, “Linear Operators, Part 1. Pure and Applied Mathematics. Vol. VII,” Interscience, New York.; Dunford-Schwartz, “Linear Operators, Part 1. Pure and Applied Mathematics. Vol. VII,” Interscience, New York.
[4] Friedman, A., Partial Differential Equations of Parabolic Type (1964), Prentice-Hall: Prentice-Hall Englewood Cliffs, N. J. · Zbl 0144.34903
[5] Lax, P., (Zarantonello, Shock Waves and Entropy Contributions to Non-linear Functional Analysis (1971), Academic Press: Academic Press New York)
[6] Rudin, W., Functional Analysis (1973), McGraw-Hill: McGraw-Hill New York · Zbl 0253.46001
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